When will the LCM of two numbers be the product of the numbers
LCM=a±b÷ab
LCM=a add b=ab
when a and b have no common factor
The least common multiple (LCM) of two numbers will be equal to the product of the two numbers when the two numbers are relatively prime, which means they share no common prime factors.
To find the LCM of two numbers, you can use the prime factorization method. Here's an explanation on how to find the LCM step by step:
1. Find the prime factors of both numbers.
Let's say we have two numbers, A and B. Find the prime factorization of A and B. For example, if A = 12 and B = 18, then the prime factorization of 12 is 2^2 * 3^1 (2 raised to the power of 2 multiplied by 3 raised to the power of 1), and the prime factorization of 18 is 2^1 * 3^2.
2. Identify the highest power of each prime factor.
Look at both prime factorizations and identify the highest power of each prime factor that appears in either number. In our example, the highest power of 2 is 2^2 and the highest power of 3 is 3^2.
3. Multiply the highest powers of prime factors.
Multiply the highest powers of each prime factor together. In our example, multiplying 2^2 and 3^2 gives us (2^2 * 3^2) = 4 * 9 = 36.
4. The result is the LCM of the two numbers.
The result of step 3 is the LCM of the two numbers, which in our example is 36. So, the LCM of 12 and 18 is 36.
In cases where the LCM of two numbers is equal to the product of the numbers, it means that the numbers are relatively prime. For example, if A = 4 and B = 7, the LCM of 4 and 7 is 28, which is equal to the product of the two numbers (4 * 7 = 28).